Economic design of multivariate Bayesian control chart with two sampling intervals

Abstract

In this paper, the economic design of a multivariate Bayesian control chart with two sampling intervals for monitoring the process mean is developed. The economic design of traditional control charts such as T2, SPRT, EWMA, and CUSUM charts with variable sampling interval (VSI) has been developed in recent years to control the industrial processes by minimizing the average cost of the process, however, it has been proved that these traditional, non-Bayesian process control charts are not optimal. There has been some limited development of the economic design of Bayesian control charts with a single sampling interval (SSI), but no results regarding the economic design of the Bayesian control chart with two sampling intervals have been reported in the literature. The objective is to find the optimal control chart parameters, namely the sample size, sampling intervals and the control limits, minimizing the total long-run expected average cost per unit time. The proposed problem is formulated and solved in the semi-Markov decision process (SMDP) framework. A numerical example is provided to illustrate the whole procedure. The effectiveness of the newly proposed control chart is demonstrated through a comparison with the multivariate Bayesian control chart with a single sampling interval as well as with a recently developed MEWMA control chart. The results indicate that the proposed control chart has a considerably better performance.